On Quasiconvexity and Relative Hyperbolic Structures

Details On Quasiconvexity and Relative Hyperbolic Structures On Quasiconvexity and Relative Hyperbolic Structures

2008-11-14

arxiv.org/abs/0811.2384v4

Mathematics

Group Theory

Version to appear in Geometriae Dedicata. Included version of Bounded Coset Penetration for general relatively hyperbolic grou

Scientific paper

Let G be a group which is hyperbolic relative to a collection of subgroups A, and it is also hyperbolic relative to a collection of subgroups B. Suppose that the collection A contains B. We characterize, for subgroups of G, when quasicovexity relative to A implies quasiconvexity relative to B. We also show that quasiconvexity relative to B implies quasiconvexity relative to A. Some applications are discussed.

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